The Gradient method [1]} uses the gradient of the model with respect to the input as the explanation: \(E_{grad}(m, \mathbf {x}, c) = \frac{\partial m(\mathbf {x})_c}{\partial \mathbf {x}}\) . This gradient describes for each input dimension how much a change in that input dimension would affect the output value \(m(\mathbf {x})_c\)  in a small neighborhood around \(\mathbf {x}\) .
InputXGradient [2]} is an extension of the Gradient method, where the gradient of the model is multiplied element-wise with the original input \(\mathbf {x}\) : \(E_{IxG}(m, \mathbf {x}, c) = \frac{\partial m(\mathbf {x})_c}{\partial \mathbf {x}} \odot \mathbf {x}\) . This is done to reduce the problem of “gradient saturation” that can occur when the Gradient method is used. This approach can also be viewed from the perspective of a linear model: the gradient is a linear approximation to the model \(m\)  in the direct neighborhood around \(x\) . The product of the weight and the corresponding feature value represents the effect of the feature on the output of this linear model.
